Title: Frequentist validation and criticism of Bayesian selective inference
Authors: Alastair Young - Imperial College London (United Kingdom) [presenting]
Daniel Garcia Rasines - Imperial College London (United Kingdom)
Abstract: As much as frequentist approaches, Bayesian inference is challenged by the problem of selective inference, where the analyst interacts with the data to select what questions about an underlying population should be addressed. A conceptual framework for selection-adjusted Bayesian inference, based on specifying explicitly the selection rule which determines when inference is provided for a particular parameter, is considered. Inference is based on the selection-adjusted posterior distribution of the parameter, obtained from a model that prepends a prior to a truncated data likelihood. We examine the repeated sampling properties of the inference, revealing non-trivial and practically significant asymptotic as well as finite repeated sampling behavior.